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Bias 16: The Ellsberg Paradox

Which bet do you prefer?

Bet on the success, which makes us €1.1 M profit and nothing otherwise, of an industrial project about which we have no information.

Bet on a stock with 50% chance to net €1M and nothing otherwise?

Which bet do you prefer?

Bet on the failure, which makes us €1.1 M profit and nothing otherwise, of an industrial project about which we have no information.

Bet on a stock with 50% chance to earn €1M and nothing otherwise?

Most of us choose, in both cases, to invest in the stock with known probabilities.

Do you see the contradiction?

We have no information on the industrial project so we will compute subjective probabilities on the chance of success for this project. As we are indifferent to bet on the success or on the failure of the project, this subjective probability may be 1/2. So, we should prefer in both cases to invest in the industrial project as its expected value is higher than the stock!

This is the uncertainty or ambiguity aversion. According to some studies in neuroeconomics (Camerer and al,2005), this bias is very close to risk aversion except that it implies fear (activation of the amygdala) contrary to risk aversion, which implies our reward system (activation of the striatum). Moreover, while our risk premium (difference between the expected value of a risky asset and our willingness to pay) is constant, our ambiguity premium (difference between the expected value of an asset whose outcome’s probability is unknown and our willingness to pay) decreases with the time (Snell,Rustichini,Levy and Glimcher,2005). Just as we learn to act optimally given the actions of others (the Nash equilibrium of game theory), by choosing repeatedly, one may be learning, slowly, to deal with ambiguity in our choices.

The following movie explains in a very pedagogical way the mechanisms of this bias, whose applications in finance and marketing are particularly relevant: